What is the extreme f(x)=4x^5-7x^2+8 ?

The extreme f(x)=4x^5-7x^2+8 is Maximum(0,8),Minimum(\sqrt[3]{7/10},4(7/10)^{5/3}-7(7/10)^{2/3}+8)

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extreme f(x)=4x^5-7x^2+8

extreme

Maximum (0, 8), Minimum (3 \frac{7}{10}, 4 (\frac{7}{10})^{\frac{5}{3}} - 7 (\frac{7}{10})^{\frac{2}{3}} + 8)

Solution steps

f^{'} (x) = 20 x^{4} - 14 x

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3 \frac{7}{10},

Increasing

: 3 \frac{7}{10} < x < \infty

Plug

x = 0

into

4 x^{5} - 7 x^{2} + 8 : 8

Maximum (0, 8)

Plug

x = 3 \frac{7}{10}

into

4 x^{5} - 7 x^{2} + 8 : 4 (\frac{7}{10})^{\frac{5}{3}} - 7 (\frac{7}{10})^{\frac{2}{3}} + 8

Minimum (3 \frac{7}{10}, 4 (\frac{7}{10})^{\frac{5}{3}} - 7 (\frac{7}{10})^{\frac{2}{3}} + 8)

Maximum (0, 8), Minimum (3 \frac{7}{10}, 4 (\frac{7}{10})^{\frac{5}{3}} - 7 (\frac{7}{10})^{\frac{2}{3}} + 8)

What is the extreme f(x)=4x^5-7x^2+8 ?
The extreme f(x)=4x^5-7x^2+8 is Maximum(0,8),Minimum(\sqrt[3]{7/10},4(7/10)^{5/3}-7(7/10)^{2/3}+8)